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p-adic Function Analysis (Lecture Notes In Pure And Applied Mathematics Ser.)
by Jose M. Bayod"Written by accomplished and well-known researchers in the field, this unique volume discusses important research topics on p-adic functional analysis and closely related areas, provides an authoritative overview of the main investigative fronts where developments are expected in the future, and more. "
p-adic Functional Analysis
by W.H. Schikhof C. Perez-Garcia Jerzy Kakol"Contains research articles by nearly 40 leading mathematicians from North and South America, Europe, Africa, and Asia, presented at the Fourth International Conference on p-adic Functional Analysis held recently in Nijmegen, The Netherlands. Includes numerous new open problems documented with extensive comments and references."
p-adic Hodge Theory (Simons Symposia #210)
by Bhargav Bhatt Martin OlssonThis proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning integral questions and their connections to notions in algebraic topology. This volume features original research articles as well as articles that contain new research and survey some of these recent developments. It is the first of three volumes dedicated to p-adic Hodge theory.
The p-adic Simpson Correspondence
by Takeshi Tsuji Michel Gros Ahmed AbbesThe p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra--namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.
P-graphs for Process Systems Engineering: Mathematical Models and Algorithms
by Ferenc Friedler Ákos Orosz Jean Pimentel LosadaThis book discusses the P-graph framework for developing and understanding effective design tools for process systems engineering, and addresses the current state of its theory and applications. The book details the new philosophy of the axioms-based mathematical modelling of processing systems, the basic algorithms, areas of application, future directions, and the proofs of theorems and algorithms. Because of the rigorous foundation of the theory, the framework provides a firm basis for future research in mathematical modelling, optimization, and design of complex engineering systems. The various P-graph applications discussed include process network synthesis, reliability engineering, and systems resilience. The framework opens new avenues for research in complex systems including redundant operations for critical infrastructure, systems sustainability, and modelling tools for disaster engineering. Demonstration software is provided to facilitate the understanding of the theory. The book will be of interest to institutions, companies, and individuals performing research and R&D in process systems engineering.
p - hacking und die Verfälschung statistischer Ergebnisse: Verbesserungsprozesse hinsichtlich Prozessbewertungen (essentials)
by Marcus HellwigDie Signifikanz einer statistischen Aussage wird mit p bezeichnet, als probabilistische Größe. Es gibt Kritik an der Aussagekraft des p-Wertes dahin, dass er in der Statistik mitunter dahingehend missbraucht wird, dass Effektgrößen bewusst verfälscht werden. Dieser Missbrauch äußert sich darin, dass an der an der Größe und Auswahl einer Datenmenge solange manipuliert wird, bis die erwünschten Parameter erreicht werden. Diese Tätigkeit wird mit - p – hacking bezeichnet. Dieses essential widmet sich der Aufklärung.
p-Laplace Equation in the Heisenberg Group
by Diego RicciottiThis works focuses on regularity theory for solutions to the p-Laplace equation in the Heisenberg group. In particular, it presents detailed proofs of smoothness for solutions to the non-degenerate equation and of Lipschitz regularity for solutions to the degenerate one. An introductory chapter presents the basic properties of the Heisenberg group, making the coverage self-contained. The setting is the first Heisenberg group, helping to keep the notation simple and allow the reader to focus on the core of the theory and techniques in the field. Further, detailed proofs make the work accessible to students at the graduate level.
Padé Methods for Painlevé Equations (SpringerBriefs in Mathematical Physics #42)
by Yasuhiko Yamada Hidehito NagaoThe isomonodromic deformation equations such as the Painlevé and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics. For discrete analogs of these equations in particular, much progress has been made in recent decades. Various approaches to such isomonodromic equations are known: the Painlevé test/Painlevé property, reduction of integrable hierarchy, the Lax formulation, algebro-geometric methods, and others. Among them, the Padé method explained in this book provides a simple approach to those equations in both continuous and discrete cases.For a given function f(x), the Padé approximation/interpolation supplies the rational functions P(x), Q(x) as approximants such as f(x)~P(x)/Q(x). The basic idea of the Padé method is to consider the linear differential (or difference) equations satisfied by P(x) and f(x)Q(x). In choosing the suitable approximation problem, the linear differential equations give the Lax pair for some isomonodromic equations. Although this relation between the isomonodromic equations and Padé approximations has been known classically, a systematic study including discrete cases has been conducted only recently. By this simple and easy procedure, one can simultaneously obtain various results such as the nonlinear evolution equation, its Lax pair, and their special solutions. In this way, the method is a convenient means of approaching the isomonodromic deformation equations.
Painless Algebra (Painless Series)
by Lynette LongDefines algebraic terms, shows how to avoid pitfalls in calculation, presents painless methods for understanding and graphing equations, and makes problem-solving fun. Titles in Barron's extensive Painless Series cover a wide range of subjects, as they are taught at middle school and high school levels. Perfect for supporting Common Core Standards, these books are written for students who find the subjects somewhat confusing, or just need a little extra help. Most of these books take a lighthearted, humorous approach to their subjects, and offer fun exercises including puzzles, games, and challenging "Brain Tickler" problems to solve. Bonus Online Component: includes additional games to challenge students, including Beat the Clock, a line match game, and a word scramble.
Painless Algebra (Barron's Painless)
by Lynette Long Ph.D.Barron's makes learning Algebra fun and PAINLESS!Painless Algebra provides lighthearted, step-by-step learning and includes:The many ways that Algebra can help you figure out practical problems in everyday lifePainless methods for understanding and graphing equations>Painless tips, common pitfalls, instructive tables, diagrams, &“brain tickler&” quizzes and answers throughout each chapter, and more.
Painless Calculus (Barron's Painless)
by Christina PawlowskiLearning at home is now the new normal. Need a quick and painless refresher? Barron&’s Painless books make learning easier while you balance home and school. Teaches basic algebra, exponents and roots, equations and inequalities, and polynomials.Titles in Barron's extensive Painless Series cover a wide range of subjects, as they are taught at middle school and high school levels. Perfect for supporting Common Core Standards, these books are written for students who find the subjects somewhat confusing, or just need a little extra help. Most of these books take a lighthearted, humorous approach to their subjects, and offer fun exercises including puzzles, games, and challenging "Brain Tickler" problems to solve. Bonus Online Component: includes additional games to challenge students, including Beat the Clock, a line match game, and a word scramble.
Painless Geometry (Painless Series)
by Lynette LongThe thought of solving theorems or postulates leaves some students quivering in their boots. . . but not anymore! <P><P>This must-have guide takes the pain out of learning geometry once and for all. The author demonstrates how solving geometric problems amounts to fitting parts together to solve interesting puzzles. <P><P>Students discover relationships that exist between parallel and perpendicular lines; analyze the characteristics of distinct shapes such as circles, quadrilaterals, and triangles; and learn how geometric principles can solve real-world problems. <P><P>Like all titles in Barron's Painless Series, this book presents informal, student-friendly approaches to learning geometry, emphasizing interesting details, outlining potential pitfalls step by step, offering "Brain Tickler" quizzes, and more.
Painless Geometry (Barron's Painless)
by Lynette Long Ph.D.Barron's makes learning Geometry fun and PAINLESS!Painless Geometry provides lighthearted, step-by-step learning and includes:Characteristics of distinct shapes, such as circles, quadrilaterals, and trianglesDiscussion on how geometric principles can solve real-world problemsPainless tips, common pitfalls, instructive tables, diagrams, &“brain tickler&” quizzes and answers throughout each chapter, and more.
Painless Pre-Algebra (Barron's Painless)
by Amy Stahl M.S. Ed.Learning at home is now the new normal. Need a quick and painless refresher? Barron&’s Painless books make learning easier while you balance home and school. Teaches basic algebra, exponents and roots, equations and inequalities, and polynomials.Titles in Barron's extensive Painless Series cover a wide range of subjects, as they are taught at middle school and high school levels. Perfect for supporting Common Core Standards, these books are written for students who find the subjects somewhat confusing, or just need a little extra help. Most of these books take a lighthearted, humorous approach to their subjects, and offer fun exercises including puzzles, games, and challenging "Brain Tickler" problems to solve. Bonus Online Component: includes additional games to challenge students, including Beat the Clock, a line match game, and a word scramble.
Painless Statistics (Barron's Painless)
by Patrick HonnerWhether you&’re a student or an adult looking to refresh your knowledge, Barron&’s Painless Statistics provides review and practice in an easy, step-by-step format.An essential resource for:Virtual learningHomeschoolLearning podsSupplementing classes/in-person learningInside you&’ll find:Clear examples for all topics, including data and distributions, basic probability, confidence intervals, bivariate statistics, and much moreDiagrams, charts, and instructive math illustrationsPainless tips, common pitfalls, and informative sidebarsMath talk boxes that translate complex &“math speak&” into easy-to-understand languageBrain Tickler quizzes throughout each chapter to test your progress
The Painlevé Handbook (Mathematical Physics Studies)
by Robert Conte Micheline MusetteThis book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schrödinger equation, the Korteweg-de Vries equation, Hénon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations. Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painlevé function; and an overview of new results since the book’s original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences.
Painlevé III: A Case Study in the Geometry of Meromorphic Connections (Lecture Notes in Mathematics #2198)
by Claus Hertling Martin A. GuestThe purpose of this monograph is two-fold: it introduces a conceptual language for the geometrical objects underlying Painlevé equations, and it offers new results on a particular Painlevé III equation of type PIII (D6), called PIII (0, 0, 4, −4), describing its relation to isomonodromic families of vector bundles on P1 with meromorphic connections. This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics. It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections. Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed. These provide examples of variations of TERP structures, which are related to tt∗ geometry and harmonic bundles. As an application, a new global picture o0 is given.
Pair-Correlation Effects in Many-Body Systems: Towards a Complete Theoretical Description of Pair-Correlations in the Static and Kinetic Description of Many-Body Systems (Springer Theses)
by Kristian BlomThe laws of nature encompass the small, the large, the few, and the many. In this book, we are concerned with classical (i.e., not quantum) many-body systems, which refers to any microscopic or macroscopic system that contains a large number of interacting entities. The nearest-neighbor Ising model, originally developed in 1920 by Wilhelm Lenz, forms a cornerstone in our theoretical understanding of collective effects in classical many-body systems and is to date a paradigm in statistical physics. Despite its elegant and simplistic description, exact analytical results in dimensions equal and larger than two are difficult to obtain. Therefore, much work has been done to construct methods that allow for approximate, yet accurate, analytical solutions. One of these methods is the Bethe-Guggenheim approximation, originally developed independently by Hans Bethe and Edward Guggenheim in 1935. This approximation goes beyond the well-known mean field approximation and explicitly accounts for pair correlations between the spins in the Ising model. In this book, we embark on a journey to exploit the full capacity of the Bethe-Guggenheim approximation, in non-uniform and non-equilibrium settings. Throughout we unveil the non-trivial and a priori non-intuitive effects of pair correlations in the classical nearest-neighbor Ising model, which are taken into account in the Bethe-Guggenheim approximation and neglected in the mean field approximation.
Pairwise Comparisons Method: Theory and Applications in Decision Making (Lecture Notes in Economics and Mathematical Systems #690)
by Jaroslav RamíkThis book examines relationships between pairwise comparisons matrices. It first provides an overview of the latest theories of pairwise comparisons in decision making, discussing the pairwise comparison matrix, a fundamental tool for further investigation, as a deterministic matrix with given elements. Subsequent chapters then investigate these matrices under uncertainty, as a matrix with vague elements (fuzzy and/or intuitionistic fuzzy ones), and also as random elements. The second part of the book describes the application of the theoretical results in the three most popular multicriteria decision-making methods: the Analytic Hierarchy Process (AHP), PROMETHEE and TOPSIS. This book appeals to scholars in areas such as decision theory, operations research, optimization theory, algebra, interval analysis and fuzzy sets.
Pairwise Multiple Comparisons: Theory and Computation (SpringerBriefs in Statistics)
by Taka-aki Shiraishi Shin-ichi Matsuda Hiroshi SugiuraThis book focuses on all-pairwise multiple comparisons of means in multi-sample models, introducing closed testing procedures based on maximum absolute values of some two-sample t-test statistics and on F-test statistics in homoscedastic multi-sample models. It shows that (1) the multi-step procedures are more powerful than single-step procedures and the Ryan/Einot–Gabriel/Welsh tests, and (2) the confidence regions induced by the multi-step procedures are equivalent to simultaneous confidence intervals. Next, it describes the multi-step test procedure in heteroscedastic multi-sample models, which is superior to the single-step Games–Howell procedure. In the context of simple ordered restrictions of means, the authors also discuss closed testing procedures based on maximum values of two-sample one-sided t-test statistics and based on Bartholomew's statistics. Furthermore, the book presents distribution-free procedures and describes simulation studies performed under the null hypothesis and some alternative hypotheses. Although single-step multiple comparison procedures are generally used, the closed testing procedures described are more powerful than the single-step procedures. In order to execute the multiple comparison procedures, the upper 100α percentiles of the complicated distributions are required. Classical integral formulas such as Simpson's rule and the Gaussian rule have been used for the calculation of the integral transform that appears in statistical calculations. However, these formulas are not effective for the complicated distribution. As such, the authors introduce the sinc method, which is optimal in terms of accuracy and computational cost.
The Palgrave Centenary Companion To Principia Mathematica
by Nicholas Griffin Bernard LinskyTo mark the centenary of the 1910 to 1913 publication of the monumental Principia Mathematica by Alfred N. Whitehead and Bertrand Russell, this collection of fifteen new essays by distinguished scholars considers the influence and history of PM over the last hundred years.
The Palgrave Companion to Harvard Economics
by Robert A. CordHarvard University has been and continues to be one of the most important global centres for economics. With three chapters on themes in Harvard economics and 41 chapters on the lives and work of Harvard economists, these two volumes show how economics became established at the University, how it produced some of the world’s best-known economists, including Joseph Schumpeter, Wassily Leontief and John Kenneth Galbraith, and how it remains a global force for the very best in teaching and research in economics. With original contributions from a stellar cast, the volumes provide economists – especially those interested in macroeconomics and the history of economic thought – with an in-depth analysis of Harvard economics.
The Palgrave Companion to Oxford Economics
by Robert A. CordThe University of Oxford has been and continues to be one of the most important global centres for economics. With six chapters on themes in Oxford economics and 24 chapters on the lives and work of Oxford economists, this volume shows how economics became established at the University, how it produced some of the world’s best-known economists, including Francis Ysidro Edgeworth, Roy Harrod and David Hendry, and how it remains a global force for the very best in teaching and research in economics. With original contributions from a stellar cast, this volume provides economists – especially those interested in macroeconomics and the history of economic thought – with the first in-depth analysis of Oxford economics.
The Palgrave Handbook of Economic Performance Analysis
by Thijs Ten Raa William H. GreeneThis Handbook takes an econometric approach to the foundations of economic performance analysis. The focus is on the measurement of efficiency, productivity, growth and performance. These concepts are commonly measured residually and difficult to quantify in practice. In real-life applications, efficiency and productivity estimates are often quite sensitive to the models used in the performance assessment and the methodological approaches adopted by the analysis. The Palgrave Handbook of Performance Analysis discusses the two basic techniques of performance measurement – deterministic benchmarking and stochastic benchmarking – in detail, and addresses the statistical techniques that connect them. All chapters include applications and explore topics ranging from the output/input ratio to productivity indexes and national statistics.
The Palgrave Handbook of Literature and Mathematics
by Nina Engelhardt Alice Jenkins Robert TubbsThis handbook features essays written by both literary scholars and mathematicians that examine multiple facets of the connections between literature and mathematics. These connections range from mathematics and poetic meter to mathematics and modernism to mathematics as literature. Some chapters focus on a single author, such as mathematics and Ezra Pound, Gertrude Stein, or Charles Dickens, while others consider a mathematical topic common to two or more authors, such as squaring the circle, chaos theory, Newton’s calculus, or stochastic processes. With appeal for scholars and students in literature, mathematics, cultural history, and history of mathematics, this important volume aims to introduce the range, fertility, and complexity of the connections between mathematics, literature, and literary theory.